Day 2: Crack the Code (Linear Equations) 🕵️♂️
Secondary Stage (Grades 9 & 10) | Apex Institute of Maths and Sciences
🎯 1. Concept: The Balancing Act
Welcome back! Yesterday we learned about variables (like x). Today, we are going to become mathematical detectives and find out exactly what number x is hiding.
An Equation is like a weighing scale. The equal sign (=) is the center. Whatever you do to one side of the equation, you MUST do to the other side to keep it balanced.
Your main mission is always the same: Isolate the variable. You want to get ‘x’ all by itself on one side of the equal sign.
💡 2. Inverse Operations
To move a number away from ‘x’, use its opposite (inverse) operation:
- Opposite of Addition is Subtraction:
If x + 5 = 12, subtract 5 from both sides. (x = 7) - Opposite of Subtraction is Addition:
If y – 4 = 10, add 4 to both sides. (y = 14) - Opposite of Multiplication is Division:
If 3m = 15 (which means 3 times m), divide both sides by 3. (m = 5)
Two-Step Example: 2x + 1 = 9. First, subtract 1 (2x = 8). Then, divide by 2 (x = 4).
🌍 3. Math in Our Daily Life
Equations help us solve real-world mysteries!
Scenario 1 (Shopping): You have exactly ₹500. You buy a shirt for ₹300 and 2 identical pairs of socks. How much did one pair of socks cost?
Equation: 2x + 300 = 500. Subtract 300 (2x = 200). Divide by 2 (x = 100). The socks cost ₹100 each!
Scenario 2 (Travel): A taxi charges a ₹50 booking fee plus ₹10 for every kilometer. If your total bill is ₹150, how far did you travel?
Equation: 10x + 50 = 150. Subtract 50 (10x = 100). Divide by 10 (x = 10). You traveled 10 km!
📝 4. Analytical Tasks
Open your math journal and complete these algebraic challenges:
- Task A: Build an Equation: Write an equation for this sentence: “Three times a number, minus four, equals fourteen.” Then solve for the number.
- Task B: Solve it: Solve the equation: 5p – 7 = 18. Show your steps (what did you add first? What did you divide by?).
- Task C: Real World: Create your own real-life word problem that matches the equation 4x + 20 = 100.
✅ 5. Day 2 Practice Test
Can you crack the code? Select the correct answers below and click submit to check your score and view the step-by-step solutions.
